Presentation on theme: "Interference and Diffraction"— Presentation transcript:
1Interference and Diffraction PY212 Lecture 25Interference and DiffractionProf. Tulika Bose12/3/09Fun Link: Diffraction with Ace Ventura
2Summary from last timeThe wave theory of light is strengthened by the interference and diffraction of light.Young’s double-slit experiment demonstrated interference.In the double-slit experiment, constructive interference occurs whenand destructive interference whenTwo sources of light are coherent if they have the same frequency and maintain the same phase relationship.
3Summary from last timeYoung realized that he could create two coherent sources of light waves that produce an interference patternThomas Young's sketch of two-slit interference,
4Summary from last timeYoung realized that he could create two coherent sources of light waves that produce an interference pattern
5Intensity distribution of double-slit interference pattern Summary from last timeIntensity distribution of double-slit interference patternNote this is not the full picture;will study diffraction today….
6Phasor AnalysisThe two waves can be added using phasors, to take the phase difference into account:
7Summary from last timeLight undergoes a 180° phase change if it reflects from a medium of higher index of refraction.
8Interference in thin films Interference effects are commonly observed in thin filmsExamples include soap bubbles and oil on waterThe varied colors observed when white light is incident on such films result from the interference of waves reflected from the two surfaces of the film
9in reality there are an infinite number of reflections. constructivedestructivein reality there are an infinite number of reflections.
10Interference in thin films A similar effect takes place when a shallowly curved piece of glass is placed on a flat one. When viewed from above, concentric circles appear that are called Newton’s rings.
11Non-reflective coatings: work for a range of wavelengths It’s purple because the visible spectrum is centered on green
12Michelson Interferometer, Schematic A ray of light is split into two rays by the mirror MoThe mirror is at 45o to the incident beamThe mirror is called a beam splitterIt transmits half the light and reflects the restThe reflected ray goes toward mirror M1The transmitted ray goes toward mirror M2The two rays travel separate paths L1 and L2After reflecting from M1 and M2, the rays eventually recombine at Mo and form an interference pattern
14Diffraction of a wave by a slit Whether waves in water or light in air, passage through a slit yields a diffraction pattern that will appear more dramatic as the size of the slit approaches the wavelength of the wave.
15Diffraction by an EdgeExaggerated viewEven without a small slit, diffraction can be strong.Simple propagation past an edge yields a diffraction pattern.
16Knife-edge diffraction pattern If a wave passes over a sharp corner, there is a diffraction pattern, that changes the intensity around the region of the geometrical shadow.We can demonstrate that with the laser and a knife edge.The wave bends around the edge, and some intensity appears in the region where we would expect a geometric shadow.Light passing by edge
17Radio waves diffract around mountains When the wavelength is km long, a mountain peak is a very sharp edge!knife-edge effect is explained by Huygens' principle:a well-defined obstruction to an electromagnetic wave acts as a secondary source, and creates a new wavefront.This new wavefront propagates into the geometric shadow area of the obstacle.
18Diffraction of sound around a sharp edge You may have noticed that if you are around the corner from a marching band, you can still hear some sound from itvbuildingWhich instrument will you hear first ?High-pitched guitar ?Low-pitched bass drum ?
19Diffraction of sound around a sharp edge The long wavelength sounds of the bass drum will diffract around the corner more efficiently than the more directional, short wavelength sounds of the higher pitched instruments.
20Introduction to diffraction patterns Since a slit consists of two edges, we have to take this into account when discussing diffraction/interference from a slit, or set of slits.In fact, waves from different parts of the opening can also interfere, so the situation is even more complicated than just the slit edges.On the next few projections we show some diffraction patterns.
21diffraction through a circular opening a laser beam passes through an opening and hits a screen
22diffraction off an object wave incident on a cylinder. the incident wave comes from above. Notice how the circular wave comes off of the cylinder asymmetrically since it strikes the top first
23Note the interference between the incoming plane-wave and the outgoing circular wave
24Diffraction pattern off of a penny The penny is between the source and the screen.Note the constructive interference at the center of the geometrical shadow region.
26Narrow slit: Fraunhofer diffraction pattern Each portion of the slit acts as a source of light waves!these different sources can interfere since they are in phase and coherent(b) If we divide the opening into halves, then the wave from the top half can interfere with the bottom half.In general the minima occur at[first minimum]
27Diffraction pattern intensity NOTE:Minima for a diffraction pattern satisfy a criterion that looks similar to that for the maxima for double-slit interferenceD is the slit width while d was the slit separationm=0 does not represent a dark fringeCentral maximum is twice as wide
28Most of the light intensity is concentrated in the central maximum Intensity as a function of angle θwhere β is the phase difference:.Most of the light intensity is concentrated in the central maximumThe graph shows a plot of light intensity vs. b/2
29Intensity of Two-Slit Diffraction Patterns When more than one slit is present, consideration must be made ofThe diffraction patterns due to individual slitsThe interference due to the wave coming from different slitsInterference term
30Intensity of Two-Slit Diffraction Patterns The diffraction factor (depends on β) appears as an “envelope” modifying the more rapidly varying interference factor (depends on δ).
31Why the central diffraction peak shown, plotted for the case where d = 6D = 60λ, contains 11 interference fringes ?
32Intensity of Two-Slit Diffraction Patterns, Graph of Pattern The broken blue line is the diffraction patternThe red-brown curve shows the cos2 termThis term, by itself, would result in peaks with all the same heightsThe uneven heights result from the diffraction term (square brackets in the equation)